Recent advances in mathematical demography strongly suggest that significant regularities characterize the behavior of all populations, and understanding those processes can play an important part in health planning. The proposed research will explore regularities associated with two major themes: the dynamic relationships between demographic rates and the size and structure of observed populations, and the analytical linkages that connect any observed population to its stable counterpart. On the first theme, the proposed work will use differentiation and differencing over time to examine marginal change in population size and structure. In populations with a single living state, efforts will be made to analyze change over several intervals of time, and to provide explicit mathematical expressions for the short to intermediate term implications of present demographic behavior. In populations where more than one living state is recognized, efforts will focus on patterns of change over a single time interval. On the second theme, three linkages between observed populations and their stable !counterparts will be examined. The first linkage is represented by "crossover points" where proportional distributions of demographic events from observed and stable populations intersect. The second linkage is population momentum, the tendency for a growing population to continue to increase in size after achieving replacement level fertility and mortality. The third linkage is represented by the Kullback distance, a measure of how far an observed population is from stability. The work will emphasize the immediately relevant connections between an observed population and its stable counterpart.